Skip to content

Physics Playground

Simulations How we teach Pricing

Language

Log in Start learning free

Loading…

Physics Playground

Built on open, peer-reviewed sources: OpenStax, The Feynman Lectures on Physics, HyperPhysics, NASA and NIST. See our sources.

Learn

Physics course
Math for Physics
Start with the math toolkit
Simulations
Glossary
Exercises
Past exams
Library
How we teach

Company

Pricing
Terms
Privacy
Contact

© 2026 Physics Playground. Made for the curious.Language

Exercises Systems of equations

Example 3 from Algebra and Trigonometry, 11.1 Systems of Linear Equations: Two Variables

Solving a System of Equations in Two Variables by Substitution

Solve the following system of equations by substitution.

\begin{array}{l} - x + y = −5 \\ 2 x - 5 y = 1 \end{array}

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
First, we will solve the first equation for $y .$

$\begin{array}{l} - x + y = −5 \\ y = x −5 \end{array}$
Now we can substitute the expression $x −5$ for $y$ in the second equation.

$\begin{array}{l} 2 x - 5 y = 1 \\ 2 x - 5 (x - 5) = 1 \\ 2 x - 5 x + 25 = 1 \\ - 3 x = −24 \\ x = 8 \end{array}$
Now, we substitute $x = 8$ into the first equation and solve for $y .$

$\begin{array}{l} - (8) + y = −5 \\ y = 3 \end{array}$
Our solution is $(8, 3) .$
Check the solution by substituting $(8, 3)$ into both equations.

$\begin{array}{l} - x + y = - 5 \\ - (8) + (3) = - 5 & True \\ 2 x - 5 y = 1 \\ 2 (8) - 5 (3) = 1 & True \end{array}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solve the following system of equations by substitution.

\begin{array}{l} x = y + 3 \\ 4 = 3 x −2 y \end{array}

How did it go?

PreviousSolving a System of Equations in Two Variables by Graphing Next Solving a System by the Addition Method

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 11.1, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.